Qudit vs. Qubit: Simulated performance of error correction codes in higher dimensions

TL;DR

This paper investigates the potential advantages of using qudits over qubits in quantum error correction, demonstrating comparable error thresholds across different dimensions through simulation of tailored circuits.

Contribution

It introduces and simulates a qudit error correction code with a multidimensional noise model, highlighting the feasibility and performance of higher-dimensional quantum systems.

Findings

Error thresholds around 10^{-4} for qudits of dimensions 2, 3, and 5

Inclusion of a flag qudit improves error protection

Higher-dimensional qudits show promise for fault-tolerant quantum computing

Abstract

Qudits can be described by a state vector in a $q$-dimensional Hilbert space, enabling a more extensive encoding and manipulation of information compared to qubits. This implies that conducting fault-tolerant quantum computations using qudits rather than qubits might entail less overhead. In this work, we investigate the viability of qudits in error correction codes by creating and simulating the quantum circuitry for the smallest qudit error correction code with a multidimensional circuit-level noise model and specifically adapted decoders. After introducing a flag qudit to protect the code from hook errors, comparable error thresholds of the order of $10^{-4}$ are obtained for qudits of dimensions $2$, $3$ and $5$.